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# Course Weekly Lecture Plan

 Week Topic 1 1st week Introduction Signals and Classification of Signals Properties of Dirac and Unit Step Functions Basic Continuous-Time Signals Basic Discrete-Time Signals Examples 2nd week Periodic signals and their representations Sampling theorem Analog to Digital Conversion Digital to Analog Conversion Introduction to signals in frequency domain Discrete time periodic signals Delay, shift and framing of the signals Examples 3rd week Convolution integral and sum Convolution of time domain signals and their applications in computer engineering Signal domains Relationships between signal domains t, kT, ?, j?, s, z System definition Transfer function of a system Examples 4th week Introduction to linear time invariant (LTI) systems Response of a Continuous-Time (CT) LTI System and the Convolution Integral Properties of CT-LTI Systems Eigenfunctions of CT-LTI Systems Systems Described by Differential Equations Delay operator for continuous time systems Stability definitions for LTI systems Examples 5th week Response of a Discrete-Time (DT) LTI System and Convolution Sum Properties of DT-LTI Systems Systems Described by Difference Equations Unit delay operator in discrete time systems Discrete system representation with unit delays Examples 6th week Realtime programming of difference equations Moving Average FIR filter example Real time programming of a DT transfer function Examples 7th week Signals and systems at j? domain Fourier and Laplace transform relationships An introduction to Laplace Transform Brief properties of Laplace transform Inverse Laplace Transform Examples 8th week Frequency response analysis of CT systems and signals Bandwidth Bode Diagrams Filtering of CT signals Introduction to Fourier Transform 9th week Fourier Series Representation of Periodic Signals Properties of Fourier series Fourier Transform Properties of the Fourier Transform Examples 10th week (Visa exam week) Applications for DT and CT Systems’ Time and Frequency Domain Response Applications for Real Time Programming of DT Systems Exam 11th week The z-Transform and Discrete-Time LTI Systems Properties of the z-Transform The Inverse z-Transform Transfer function of systems in z domain Real time Programming transfer functions in z domain Examples 12th week Digital filtering Common digital filter structures Frequency response analysis of the digital filters Real time programming of digital filters Examples 13th week Frequency response analysis of the digital systems Fourier Analysis of Discrete-Time Signals and Systems Discrete Fourier Series Discrete Fourier Transform (DFT) Examples 14th week Frequency Response of Discrete-Time LTI Systems Fast Fourier Transform (FFT) DFT and FFT algorithms A brief introduction to Wavelet Transform Comparison of DFT, FFT, STFT and wavelets Examples 15th week Introduction to state space analysis Transfer functions in state space State Space Representation of Discrete-Time LTI Systems Space Representation of Continuous-Time LTI Systems Real time programming of discrete time systems Examples 2 1st week Introduction Signals and Classification of Signals Properties of Dirac and Unit Step Functions Basic Continuous-Time Signals Basic Discrete-Time Signals Examples 2nd week Periodic signals and their representations Sampling theorem Analog to Digital Conversion Digital to Analog Conversion Introduction to signals in frequency domain Discrete time periodic signals Delay, shift and framing of the signals Examples 3rd week Convolution integral and sum Convolution of time domain signals and their applications in computer engineering Signal domains Relationships between signal domains t, kT, ?, j?, s, z System definition Transfer function of a system Examples 4th week Introduction to linear time invariant (LTI) systems Response of a Continuous-Time (CT) LTI System and the Convolution Integral Properties of CT-LTI Systems Eigenfunctions of CT-LTI Systems Systems Described by Differential Equations Delay operator for continuous time systems Stability definitions for LTI systems Examples 5th week Response of a Discrete-Time (DT) LTI System and Convolution Sum Properties of DT-LTI Systems Systems Described by Difference Equations Unit delay operator in discrete time systems Discrete system representation with unit delays Examples 6th week Realtime programming of difference equations Moving Average FIR filter example Real time programming of a DT transfer function Examples 7th week Signals and systems at j? domain Fourier and Laplace transform relationships An introduction to Laplace Transform Brief properties of Laplace transform Inverse Laplace Transform Examples 8th week Frequency response analysis of CT systems and signals Bandwidth Bode Diagrams Filtering of CT signals Introduction to Fourier Transform 9th week Fourier Series Representation of Periodic Signals Properties of Fourier series Fourier Transform Properties of the Fourier Transform Examples 10th week (Visa exam week) Applications for DT and CT Systems’ Time and Frequency Domain Response Applications for Real Time Programming of DT Systems Exam 11th week The z-Transform and Discrete-Time LTI Systems Properties of the z-Transform The Inverse z-Transform Transfer function of systems in z domain Real time Programming transfer functions in z domain Examples 12th week Digital filtering Common digital filter structures Frequency response analysis of the digital filters Real time programming of digital filters Examples 13th week Frequency response analysis of the digital systems Fourier Analysis of Discrete-Time Signals and Systems Discrete Fourier Series Discrete Fourier Transform (DFT) Examples 14th week Frequency Response of Discrete-Time LTI Systems Fast Fourier Transform (FFT) DFT and FFT algorithms A brief introduction to Wavelet Transform Comparison of DFT, FFT, STFT and wavelets Examples 15th week Introduction to state space analysis Transfer functions in state space State Space Representation of Discrete-Time LTI Systems Space Representation of Continuous-Time LTI Systems Real time programming of discrete time systems Examples

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